Zulip Chat Archive

Stream: Is there code for X?

Topic: diameter of a ball


Ruben Van de Velde (Dec 01 2023 at 17:32):

I found docs#Metric.diam_ball but this is an inequality. Am I wrong to expect that the equality holds (under appropriate conditions)?

Alex J. Best (Dec 01 2023 at 17:50):

There would be many examples where this fails for arbitrary (even complete) metric spaces, a quick google suggests that normed vector space is sufficient but I couldn't find that in mathlib

Junyan Xu (Dec 01 2023 at 18:35):

Maybe adapt the proof of docs#closure_ball

Jireh Loreaux (Dec 01 2023 at 19:00):

I think not too long ago @Alex Kontorovich was interested in the conditions under which the closure of any open ball is the corresponding closed ball, which is not exactly the same, but seems related, as Junyan Xu notes.

Yaël Dillies (Dec 01 2023 at 19:46):

This is more or less the same question, yes. It all depends on whether 1 is a limit point of d(x, y) when y ranges over all points.


Last updated: Dec 20 2023 at 11:08 UTC